Question
Suppose \( f(x)=3 x^{2}+1 \) and \( g(x)=2 x-4 \) Find the value of \( f(g(1)) \). 510 13 11
Ask by Chambers John. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(g(1)) = 13 \)
Solution
To find the value of \( f(g(1)) \), follow these steps:
1. **Compute \( g(1) \):**
\[
g(x) = 2x - 4
\]
\[
g(1) = 2(1) - 4 = 2 - 4 = -2
\]
2. **Compute \( f(g(1)) = f(-2) \):**
\[
f(x) = 3x^2 + 1
\]
\[
f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13
\]
**Final Answer:** \( 13 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find \( f(g(1)) \), we first need to calculate \( g(1) \). Starting with: \[ g(x) = 2x - 4 \] Substituting \( x = 1 \): \[ g(1) = 2(1) - 4 = 2 - 4 = -2 \] Next, we find \( f(g(1)) = f(-2) \). Using the function: \[ f(x) = 3x^{2} + 1 \] Substituting \( x = -2 \): \[ f(-2) = 3(-2)^{2} + 1 = 3(4) + 1 = 12 + 1 = 13 \] Thus, the value of \( f(g(1)) \) is \( \boxed{13} \).
